Towards the Thermodynamics of Localization Processes

Details Towards the Thermodynamics of Localization Processes Towards the Thermodynamics of Localization Processes

1999-07-29

arxiv.org/abs/cond-mat/9907463v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 8 figures submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.62.3429

We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger [V. Latora, M. Baranger, Phys. Rev.Lett. 82, 520(1999)] found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear in time regime of entropy increase, namely a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the non-extensive entropic indicator recently advocated by Tsallis [ C. Tsallis, J. Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that with the adoption of the ``magic'' value q = Q = 1/2 the Kolmogorov regime becomes more extended and more distinct than with the traditional entropic index q = 1. We adopt a two-site model to explain these properties by means of an analytical treatment and we argue that Q =1/2 might be a typical signature of the occurrence of Anderson's localization.

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